Abstract:
The solvability of the problem optimal control by coefficient of the highest derivative and the quantum potential in a nonlinear and nonstationary Schrödinger-type equation studded, this equation generalized the will know quantum mechanical equation. The problem of simultaneously control by several coefficients of the state equation respect to criterion of quality, which is a discrepancy of the boundary data of the solution considered. For this problem, conditions for the well posed of the problem statement founded and the existence theorem for a solution proved. We also consider a problem with a "perturbed" performance criterion, for which a theorem of the existence and uniqueness of a solution proved. In conclusion, the first variation of the quality functional defined and an iterative algorithm for solving the problem studded. The results are new for the standard Schrödinger equation also.
Keywords:Solvability of control problem, Schrödinger-type equation, optimal control, control of quantum processes, control by coefficients of equation.
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